It's been a few years since we were at Disney World with our kids. We stayed on site and I remember waiting for buses to take you from one theme park to another and then back to where you were staying. I don't remember how far apart things are and if it would be practical for a family to bike from one part of the property to another.
I know it's not designed for bikes but lets say there were bike paths connecting all the on-site hotels with the theme parks and downtown disney, would the distances be manageable?
Would certainly be preferable to having to rent a car or wait for shuttles all the time.
FWIW I think going to Disney can be a very enjoyable experience if you know what to expect and avoid the busy times of year. It is one place where kids feel like first class citizens. They get their own personalized key cards to the rooms. My daughter got made up as princess Ariel in one of the stores and when she returned to the hotel, the entire staff bowed as she entered the lobby. She'll never forget it.
It's also not hard to find a lot wrong with Disney as a company and even with the images they promote.